C#-Code

using System;
using System.Linq;

DateTime start = new(2021, 2, 12); // C# 9.x
DateTime end = new(2999, 12, 31);

while (start <= end)
{
    var s = start.ToShortDateString().Replace(".", "");
    if (s == string.Join("", s.Reverse()))
        Console.WriteLine(start.ToShortDateString());
    start = start.AddDays(1);
}

C#-Code

using System;

namespace DatumPalindrome
{
    class Program
    {
        static void Main(string[] args)
        {
            DateTime startDate = DateTime.Now;
            DateTime endDate = new DateTime(2999, 12, 31);
            DateTime iterationDay = startDate;
            int counter = 0;
            while(iterationDay < endDate)
            {
                char[] date = iterationDay.ToString("yyyyMMdd").ToCharArray();
                if (date[0] == date[7] && date[1] == date[6] && date[2] == date[5] && date[3] == date[4])
                {
                    Console.WriteLine(iterationDay.ToString("yyyy/MM/dd"));
                    counter++;
                }
                iterationDay = iterationDay.AddDays(1);
            }
            Console.WriteLine($"Anzahl: {counter}");
        }
    }
}

C#-Code

using static System.Console; //VS 2019 .Net 5.0.2

System.Text.StringBuilder sb = new System.Text.StringBuilder();

int[] tage_im_monat = new int[] { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 30 };
int start = 000, end = 10000;

static string sx(string s, int x) => s.Length == x ? s : sx("0" + s, x);

int count = 0;
for (var i = start; i < end; i++)
    for (var j = 0; j < tage_im_monat.Length; j++)    {
        string sm = sx((j + 1).ToString(), 2);
        for (var k = 0; k < tage_im_monat[j]; k++)    {
            string st = sx((k + 1).ToString(), 2);
            string temp = st + sm + sx(i.ToString(), 4);
            bool bo_palindrom = true;
            for (var l = 0; l < 4; l++)
                if (temp[l] != temp[temp.Length - 1 - l])
                    bo_palindrom = false;
            if (bo_palindrom)
            {
                WriteLine($"{++count,3}: {temp}    {int.Parse(temp.Substring(4)),4}");               
                sb.Append($"{temp}, ");
            }
        }        
    }
//System.IO.File.WriteAllText("erg_palindrom.txt", sb.ToString());
ReadKey();